Is MacBeth mad?

In MacBeth; act two, scene one, MacBeth is definitely mad.
this is shown because in the scene MacBeth is seen talking to himself about murdering king Duncan. I know he is mad because of what he says in the scene. "Is this a dagger that i see before me? The handle toward my hand? come, let me clutch thee".(2.1- lines 33-34) In this scene MacBeth is clearly hallucinating a dagger in front of him and a quote that he will say later prooves this. "I dont have you but i can see you. Fatefull Apparition, isnt it possible to touch you as well as see you? or are you nothing more than a dagger of the mind, a hallucination of my fevered brain?"(2.1-lines37-39). this prooves that he is mad because he speaks of how he has  a "fevered brain" , this is a sign that he is sick and that is why he is seeing things.